Capital spending, a key barometer of future economic growth, is expected to start picking up during the second half this year, helping to sustain the economic recovery, the government said yesterday.

For the full year, businesses' plans for spending on plant and equipment will total 3.1 percent less than in 1982, the Commerce Department said. Last spring, it was forecast that the decline in 1983 would be 3.4 percent. Expected third- and fourth-quarter increases in capital purchasing account for the upward revision, Commerce said.

So far, capital spending has lagged behind the large gains in consumer spending and home buying, both of which took off earlier in the year. Spending on plant and equipment is important because it leads to long-term expansion of the economy and not just short-term increases, and reflects business confidence.

It isn't unusual during a recovery for business spending to lag about six months behind the trough of the recession, which was reached last November.

"We're right at the moment of truth," which will determine whether the recovery will be sustained beyond this year, said Robert Ortner, Commerce Department chief economist. He said capital spending declined during the first quarter, leveled off during the second and is beginning to build during the third quarter. "It's the one area in the economy that's been a problem," Ortner said.

U.S. nonfarm businesses plan to spend $306.6 billion for new plant and equipment this year, Commerce said. The results were from a survey of businesses conducted this summer by the government.

Spending was $316.4 billion in 1982, 1.6 percent lower than the previous year.

In April and May, businesses said they planned to spend $305.5 billion this year, which was 3.4 percent less than they spent last year. Manufacturing industries accounted for most of the change in spending plans since the spring, Commerce said.

Current-dollar spending declined 3.3 percent in the first quarter. Business had planned for a 3.1 percent second-quarter increase, but spending stayed about the same as in the first quarter. Government estimates now predict a 6.7 percent current-dollar increase in the third quarter and a 4.4 percent rise in the fourth quarter.

Manufacturing industries plan a 4.8 percent decline in current-dollar spending this year, compared with an earlier forecast of a 5.8 percent decline, the government said. The largest drops in planned spending are for aircraft, 16 percent; iron and steel, 14.9 percent, and fabricated metals, 13.3 percent.

Nonmanufacturing industries plan a 2.1 percent decline, the same as predicted earlier, with the largest drop in mining, 17.8 percent; railroads, 14.5 percent; gas utilities, 9.7 percent, and air transportation, 4.6 percent.